Auto calibration method and system

Abstract

An auto calibration method according to at least one example embodiment may include receiving at least one internal equation, input data associated with a semiconductor device design, and hardware data associated with the semiconductor device design, generating at least one approximation function based on the input data and the hardware data, determining at least one loss function based on the generated at least one approximation function, determining at least one parameter of the at least one approximation function and at least one parameter of the at least one internal equation such that a value of the loss function is 0, and selectively adjusting the semiconductor device design based on the determined at least one parameter of the at least one approximation function and the at least one parameter of the at least one internal equation.

What is claimed is: 
     
         1 . An auto calibration method comprising:
 receiving at least one internal equation, input data associated with a semiconductor device design, and hardware data associated with the semiconductor device design;   generating at least one approximation function based on the input data and the hardware data;   determining at least one loss function based on the generated at least one approximation function;   determining at least one parameter of the at least one approximation function and at least one parameter of the at least one internal equation such that a value of the loss function is 0; and   selectively adjusting the semiconductor device design based on the determined at least one parameter of the at least one approximation function and the at least one parameter of the at least one internal equation.   
     
     
         2 . The auto calibration method of  claim 1 , wherein the at least one internal equation includes a partial differential equation (PDE). 
     
     
         3 . The auto calibration method of  claim 1 , wherein the determining the at least one loss function based on the generated at least one approximation function further comprises:
 determining a first loss function by applying the at least one approximation function to the at least one internal equation.   
     
     
         4 . The auto calibration method of  claim 1 , wherein the determining the at least one loss function based on the generated at least one approximation function further comprises:
 determining a second loss function by comparing the at least one approximation function to the hardware data.   
     
     
         5 . The auto calibration method of  claim 1 , wherein the determining the at least one loss function based on the generated at least one approximation function further comprises:
 determining a third loss function by comparing the at least one approximation function to at least one boundary condition of the at least one internal equation.   
     
     
         6 . The auto calibration method of  claim 1 , wherein the determining the at least one parameter of the at least one approximation function and the at least one parameter of the at least one internal equation further comprises:
 determining the at least one loss function based on a gradient descent algorithm.   
     
     
         7 . The auto calibration method of  claim 6 , wherein the determining the at least one parameter of the at least one approximation function and the at least one parameter of the at least one internal equation further comprises:
 simultaneously determining the at least one parameter of the at least one approximation function and the at least one parameter of the at least one internal equation.   
     
     
         8 . The auto calibration method of  claim 6 , wherein the determining the at least one parameter of the at least one approximation function and the at least one parameter of the at least one internal equation further comprises:
 configuring the at least one parameter of the at least one internal equation in a vector form to determine a plurality of solutions of the at least one parameter of the at least one internal equation.   
     
     
         9 . The auto calibration method of  claim 1 , wherein the determining the at least one parameter of the at least one approximation function and the at least one parameter of the at least one internal equation further comprises:
 fixing the at least one parameter of the at least one internal equation to determine the parameter included in the at least one approximation function; and   randomizing the at least one parameter of the at least one internal equation to determine the at least one parameter included in the at least one approximation function and the at least one parameter of the at least one internal equation.   
     
     
         10 . The auto calibration method of  claim 9 , wherein
 the fixing of the at least one parameter of the at least one internal equation further comprises,   performing the determining the at least one parameter included in the at least one approximation function such that the at least one parameter included in the at least one approximation function approximates the at least one internal equation; and   the randomizing of the at least one parameter of the at least one internal equation to determine the at least one parameter included in the at least one approximation function and the at least one parameter of the at least one approximation function further comprises,   determining the at least one parameter included in the at least one approximation function and the at least one parameter of the at least one internal equation so as to approximate the hardware data.   
     
     
         11 . A system comprising:
 non-transitory storage medium storing computer readable instructions; and   processing circuitry configured to execute the computer readable instructions to perform the auto calibration method of  claim 1 .   
     
     
         12 . A non-transitory computer-readable storage medium storing computer readable instructions, which when executed by processing circuitry, causes the processing circuitry to:
 receive at least one internal equation, input data associated with a semiconductor device design, and hardware data associated with the semiconductor device design;   generate at least one approximation function based on the input data and the hardware data;   determine at least one loss function based on the generated at least one approximation function;   determine at least one parameter of the at least one approximation function and at least one parameter of the at least one internal equation such that a value of the loss function is 0; and   selectively adjust the semiconductor device design based on the determined at least one parameter of the at least one approximation function and the at least one parameter of the at least one internal equation.   
     
     
         13 . An auto calibration system comprising:
 processing circuitry configured to,
 receive at least one internal equation associated with a semiconductor device design and hardware data associated with the semiconductor device design as inputs; 
 generate at least one approximation function based on the hardware data; 
 generate at least one loss function based on the at least one approximation function; 
 determine at least one parameter of the at least one approximation function and at least one parameter of the at least one internal equation such that the generated at least one loss function is 0; and 
 selectively adjust the semiconductor device design based on the determined at least one parameter of the at least one approximation function and the at least one parameter of the at least one internal equation. 
   
     
     
         14 . The auto calibration system of  claim 13 , wherein the processing circuitry is further configured to:
 generate the at least one approximation function using a deep learning network such that the hardware data is satisfied.   
     
     
         15 . The auto calibration system of  claim 13 , wherein the processing circuitry is further configured to:
 generate the at least one loss function based on the at least one approximation function; and   simultaneously learn the at least one parameter of the at least one approximation function and the at least one parameter of the at least one internal equation such that output of the at least one loss function is 0.   
     
     
         16 . The auto calibration system of  claim 15 , wherein the processing circuitry is further configured to:
 output each of a first loss function determined by applying the at least one approximation function to the at least one internal equation, a second loss function determined by comparing the at least one approximation function to the hardware data, and a third loss function determined by comparing the at least one approximation function to at least one boundary condition of the at least one internal equation.   
     
     
         17 . The auto calibration system of  claim 16 , wherein the processing circuitry is further configured to:
 determine the at least one parameter of the at least one approximation function and the at least one parameter of the at least one internal equation such that a sum of the first loss function, the second loss function, and the third loss function is 0.   
     
     
         18 . The auto calibration system of  claim 15 , wherein the processing circuitry is further configured to:
 determine the at least one loss function based on a gradient descent algorithm.   
     
     
         19 . The auto calibration system of  claim 15 , wherein the processing circuitry is further configured to:
 configure the at least one parameter of the at least one internal equation in a vector form to determine a plurality of solutions of the at least one parameter of the at least one internal equation.   
     
     
         20 . The auto calibration system of  claim 15 , wherein the processing circuitry is further configured to:
 fix the at least one parameter of the at least one internal equation to determine the at least one parameter included in the at least one approximation function; and   randomize the at least one parameter of the at least one internal equation to determine the at least one parameter included in the at least one approximation function and the at least one parameter of the at least one internal equation.